Question: Reduce to lowest terms: $ \dfrac{7}{8} \div \dfrac{8}{7} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{8}{7}$ is $ \dfrac{7}{8}$ Therefore: $ \dfrac{7}{8} \div \dfrac{8}{7} = \dfrac{7}{8} \times \dfrac{7}{8} $ $ \phantom{ \dfrac{7}{8} \times \dfrac{7}{8}} = \dfrac{7 \times 7}{8 \times 8} $ $ \phantom{ \dfrac{7}{8} \times \dfrac{7}{8}} = \dfrac{49}{64} $